I have a question about this problem.

If f(x,y,z) = 0 and g(x,y,z) = 0, show that these three fractions are equal:

$\displaystyle \frac{dx}{\frac{\partial(f,g)}{\partia l(y,z)}}$

$\displaystyle \frac{dy}{\frac{\partial(f,g)}{\partial(z,x)}}$

$\displaystyle \frac{dz}{\frac{\partial(f,g)}{\partia l(x,y)}}$

I know dF and dG both equal zero, but setting them both equal to zero and using Jacobians does not get me to the final answer. I don't know what else to try. Any help would be greatly appreciated!

I do not know how to get rid of those 68.. numbers.. btw